Pith Number

pith:FU4PK6WH

pith:1999:FU4PK6WH2GPUF7PEMP7KWPZK35

not attested not anchored not stored refs pending

The Complex Time WKB Approximation And Particle Production

A.Shaw, B.Modak, S.Biswas

arxiv:astro-ph/9902135 v1 · 1999-02-09 · astro-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{FU4PK6WH2GPUF7PEMP7KWPZK35}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:40:13.409171Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2d38f57ac7d19f42fde463feab3f2adf531291ef15dbcb8ebfaba1d3494be77c

Aliases

arxiv: astro-ph/9902135 · arxiv_version: astro-ph/9902135v1 · doi: 10.48550/arxiv.astro-ph/9902135 · pith_short_12: FU4PK6WH2GPU · pith_short_16: FU4PK6WH2GPUF7PE · pith_short_8: FU4PK6WH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/FU4PK6WH2GPUF7PEMP7KWPZK35 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 2d38f57ac7d19f42fde463feab3f2adf531291ef15dbcb8ebfaba1d3494be77c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e08bd0738aec55b2d4cf8bc4dd10c3f00d0c355c7907bc5248adfaca4fbee2b8",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1999-02-09T10:34:37Z",
    "title_canon_sha256": "76f1db86b6bed3a8d5f0980d552d36cf9731b2368cb9eb74dfe4ba5d50986bcd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9902135",
    "kind": "arxiv",
    "version": 1
  }
}